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Conjectures and Theorems in the Theory of Entire Functions
, 2000
"... Motivated by the... The main result of this paper establishes new moment inequalities for a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the LaguerrePólya class and the Riemann zetafunction. ..."
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Motivated by the... The main result of this paper establishes new moment inequalities for a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the LaguerrePólya class and the Riemann zetafunction.
Karlin’s conjecture and a question of Pólya
"... ABSTRACT. The paper answers an old question of Pólya involving Descartes ’ Rule of Signs and a related conjecture of Karlin involving the signs of Wronskians of entire functions and their derivatives. Counterexamples are given along with classes of functions for which the conjecture is valid. 0. In ..."
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ABSTRACT. The paper answers an old question of Pólya involving Descartes ’ Rule of Signs and a related conjecture of Karlin involving the signs of Wronskians of entire functions and their derivatives. Counterexamples are given along with classes of functions for which the conjecture is valid. 0. Introduction. The purpose of this paper is to answer an old unsolved question of Pólya (c. 1934) and to resolve a related conjecture of Karlin (c. 1967). In Section 1 we state Pólya’s question, Karlin’s conjecture, provide some background information and recall the definitions and terminology that will be used in the sequel. For a general
Counterexamples to a Problem of Pólya and to a Problem of Karlin
 Karlin, East J. Approx
, 1998
"... Simple counterexamples to two open problems, due to P'olya and to Karlin, discussed very recently in [4], are given. 1 ..."
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Simple counterexamples to two open problems, due to P'olya and to Karlin, discussed very recently in [4], are given. 1